Bounded sets of sheaves on compact Kaehler manifolds
Complex Variables
2017-08-23 v3 Algebraic Geometry
Abstract
We show that any set of quotients with fixed Chern classes of a given coherent sheaf on a compact Kaehler manifold is bounded in a sense which we define. The result is proved by adapting Grothendieck's boundedness criterium expressed via the Hilbert polynomial to the Kaehler set-up. As a consequence we obtain the compactness of the connected components of the Douady space of a compact Kaehler manifold.
Cite
@article{arxiv.1103.5835,
title = {Bounded sets of sheaves on compact Kaehler manifolds},
author = {Matei Toma},
journal= {arXiv preprint arXiv:1103.5835},
year = {2017}
}
Comments
Minor corrections in v2